In 2021, Rodríguez made 12 appearances with Chunichi's main team, posting a 1–4 record and 3.65 ERA with 61 strikeouts in 61+2⁄3 innings pitched.

On March 28, 2023, Rodríguez unilaterally left the Dragons to seek a contract with a Major League Baseball (MLB) team.

[4][5] On October 5, Rodríguez was officially released by Chunichi, and it was reported that he would look to sign an MLB contract.

[9] As a reliever, Rodríguez throws a fastball topping out at 100 miles per hour (161 km/h) and a slider as his two primary pitches.

[11] He started the first game of the 2023 World Baseball Classic for Cuba, striking out six and giving up one run in four innings against the Netherlands.